Posted by Melody on Thursday, October 15, 2009 at 2:51am.
I have another question I am stuck on that follows a previous question. How do I get an equation for the height of the car on the ferris wheel over a 10 minute period if we start the analysis one minute into the ride.
Can I still use the original formula
h = -35cos(2pi*X/5)+37
I don't understand what part changes to make it one minute into the ride. Appreciate any help, orignal question below.
have a trig question regarding a ferris wheel, radius 35m, axles 37m, clockwise direction, rotates twice every 10 mins. I have calculated the following function:
h = -35cos(2pi*X/5)+37
I have calculated at what height I would be after 3 minutes by substituting X=3 in the above equation. However, I need to calculate at what times I would be 30m off the ground. Can you please tell me if I am on the right track and how to calculate the time?
Maths - Reiny, Tuesday, October 13, 2009 at 8:28am
I agree with your equation, so let' set it equal to 30
30 = -35cos(2pi*X/5)+37
-7 = -35cos(2pi*X/5)
.2 = cos(2pi*X/5)
take the inverse cosine to get
2pi*X/5 = 1.369438
x = 1.09 minutes
check it by repeating the same steps you did finding the height at 3 minutes.
Math - Reiny, Thursday, October 15, 2009 at 11:12am
I am not too sure what you mean by "if we start the analysis one minute into the ride"
Where do you want the chair to be at 1 minute. The way it is, the chair would be 26.2 m high, (which also confirms my answer of 30 m at 1.09 minutes)
Do you want the chair to be at a minimum height of 2 m when the time is 1 minute?
If that is the case, we will have to perform a phase shift on our equation.
So we want h = 2 at t=1, rather than t=0
this will do it:
h = -35cos(2pi/5)(X-1) + 37
check: remember it takes 5 minutes for one rotation.
t = 1, h = 2 , at the bottom
t = 2.25 , h = 37, the height of the axle, check!
t = 3.5, h = 72 , the height of axle + radius of wheel, check!
t = 4.75, h = 37 , coming down, height of axle, check!
t = 6 , h = 2, back at the bottom, check!
In the original equation, using t values of 0, 1.25, 2.5, 3.75 and 5 will yield the same heights.
(That is how I checked if your equation was valid)
BTW, I gave you a time of 1.09 minutes for a height of 30 m.
That would be on the way up, of course you would reach another height of 30 m on your way down, which would be at (5-1.09) or 3.91 min.
repeatedly adding 5 minutes to these answers would produce all the times that the chair is 30 m high.
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